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Math Help - Series problems

  1. #1
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    Series problems

    I have two problems: 1. I have to give examples of series Xk and Yk which are conditionally convergent and Xk < ((-1)^(k+1))/k and (-1)^(k+1)Yk < 1/k. What could them be? 2. We know that Sn = ΣXk (k=1 -> n), An = Sn/n = 1/n*ΣXk (k=1 -> n) and limXn= b∈ℝ as n -> ∞. What can be said about limAn as n -> ∞?
    Last edited by antero; March 23rd 2010 at 11:23 AM.
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  2. #2
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    Help me, please!
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  3. #3
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    Both |X_k| and |Y_k| must be less than \frac{1}{k} and be conditionally convergent. The easiest example of this is X_k = \frac{(-1)^k}{ck} where c is a positive real number greater than 1.
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